Ladislaus mentioned an interesting case in another thread that I wanted to address without derailing the subject of the thread. He said:
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As for a sanatio in radice of an illegitimate election, I do not buy it.  One of the sedevacantist posters here cited the historical example of a legitimate pope who was hauled off and imprisoned; then another was elected in his place and received "universal adherence".  I do not believe that the subsequent universal adherence could effectively depose the legitimately-reigning pope.  There's a very fine line between this and conceding that the Church can in fact depose popes.

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This sounds like you are talking about Pope Martin I. I believe his case comes up now and then in this forum. He was arrested by the Byzantine emperor and hauled off to the remote area of the Crimea. The problem is that another pope was elected before he was dead.
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My recollection is that the records of this event are extremely fragmentary (he was arrested in 653), but I think most Church historians think he left behind a post-dated resignation letter, or instructions to his cardinals that they should consider him to have resigned if he did not return within some length of time, so that the papacy would not be held up by him being in exile. Once the time elapsed that he had instructed them to wait, the cardinals proceeded to an election.
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I can try to dig up some records on this, but that's my recollection of what I researched about this strange case. But obviously the cardinals could not and did not elect another pope while there was one still living, regardless of where he was.

I forget who it was who cited these case, and he also cited another one.

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We're really going to need the name of that other pope too ... But as far as I know, this is the only such case in 2,000 years.
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Let's say he did not leave any such notice of resignation, but just disappeared.  After some time, the Cardinals PRESUMED him dead, and elected a new pope.  But the actual Pope was still alive.  What would the status of that second Pope be?

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I believe this case to be impossible. In any case, as far as I know it has never happened. It seems clear that Cardinal Billot certainly didn't think such a thing to be possible.
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See, I believe that there could be material error or error of fact with regard to the identity of the Pope.  During the so-called Great Western Schism, with the 3 reigning "popes," the Church as a whole was uncertain about who the true pope was.  Despite the uncertainty by the Church, there was still among the three one who was still the legitimate pope.

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This is fundamentally different from the whole Church believing someone to be the pope who actually isn't. This is more like the whole Church not knowing who the pope is. Then nobody would really have certitude about who the rule of Faith was (the pope's Faith obviously being the rule for everyone else), with the result being that there wasn't a rule of Faith in practical terms, something that happens every time a pope dies. You are positing a situation in which the whole Church is being guided by a rule of Faith which is in fact false. Cardinal Billot does not admit this possibility because it would lead to the whole Church being led into error by following the teaching of Christ about the papacy. I suppose the problem could be mitigated by supposing that the false pope is not a heretic, but only the result of an innocent mistake, but in any case it seems to me that Cardinal Billot didn't think this could happen.
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This notion of sanatio in radice doesn't make sense to me at all.  I can see arguing that, if the Church recognizes a man universally, then it's a clear SIGN that he was really the pope, but I don't see how recognition can turn a non-pope into a pope.  cuм ex seems to teach the contrary.

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We are certainly in murky waters here. I should really read more Cardinal Billot and less CathInfo forum. Then I might actually know something about this.
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I do agree that there does appear to be a difference between what cuм ex says or implies, and what Cardinal Billot says. After the Three Days of Darkness (or pick your restoration event) I'm sure all these kinks will get ironed out, along with a complete set of instructions of what to do next time. I hope I survive until then (by "then" I mean until the restoration, not until the next time we have a pope crisis. I've had enough pope crisis to last me another thousand years).
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The Catholic Encyclopedia also posits the resignation of Pope Martin I but without any evidence.  At that point in time no pope had ever resigned despite other cases of imprisonment and/or exile.  So I don't think resignation can be presumed.  On the other hand, it's possible that the Roman clergy assumed that Pope Martin had been put to death.

From the Catholic Encyclopedia (http://www.newadvent.org/cathen/05598a.htm, St. Pope Eugene I):


This timeline is confirmed by the Liber Pontificalis.

Summary:
Jul 21, 649 - Pope Martin I elected
Jun 18, 653 - Pope Martin I arrested by agents of emperor Constans and carried off into exile
May 15, 654 - Arrived in modern day Crimea region
Aug 10, 654 - Pope Eugene I elected
Sep 16, 655 - Pope Martin I died (could also be Nov 12, 655)

As for other possible examples, refer to "Saeculum obscurum", the period where the legitimacy of the popes was sometimes shrouded in scandal.  In particular there was a lot of confusion concerning the succession around John XII, Leo VIII, and Benedict V.

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Thank you, Clemens. This was a very interesting response. Yes, the Liber Pontificalis does show an overlap between those two popes, but I'm not sure if that is supposed to be interpreted as there being two popes at the same time, or merely indicating that St. Martin was still alive when his successor was elected.
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I don't exactly follow the problem with the election of John XII. Regarding Leo VIII, it appears that he started out as an anti-pope and then later became a true pope. Bizarre career path, I know, but the 10th century was sort of like what you would get if you asked the producer who made the Godfather series to dramatize Cardinal Billot's De Ecclesia into an action movie. Novus Ordo Watch wrote a really interesting article on that wild series of events: https://novusordowatch.org/2019/12/was-pope-john12-deposed/ Relevant is the quote: "To make matters worse, the dates given for their respective reigns overlap so that Leo’s cuts into John’s and Benedict’s into Leo’s. Obviously, these dates cannot be taken as referring to definitely valid pontifical reigns, as there can only be one Pope at a time." Later on he specifies, "But there is one incident that is probably most responsible for giving Leo’s claim to the Papacy any extent of credibility at all: Pope Benedict V appears to have voluntarily resigned the Papacy in favor of Leo when the latter demanded to be recognized as Pope and presumed to depose Benedict."
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But I do believe it is a matter of faith that there can be only one pope at a time, and I believe the magisterium has taught that a pope retains office until death, resignation, or defection from the Faith.
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In any case, given the chaos of that time period and the lack of detailed information, I'm not sure what conclusions can be drawn from these events, especially when there doesn't seem to be a clear contradiction of what I said.

Let's say he did not leave any such notice of resignation, but just disappeared.  After some time, the Cardinals PRESUMED him dead, and elected a new pope.  But the actual Pope was still alive.  What would the status of that second Pope be?

I can't cite anything, but doesn't canon law have a "tacit resignation of office" clause?  I mean, if someone just walks away from his duties, it is legally logical to assume he resigned.  (This assumes a proper amount of time was involved).  I would think the 2nd pope would be valid and true, even if the original one showed up one day.

Why don't you enlighten us as to what (you think) the peaceful an universal acceptance means.  And then provide a quote or two to support it.  

We can all agree that this acceptance must be made by actual Catholics.

We can all agree that this acceptance must be made by actual Catholics.

Agreed.  Sedevacantist's vote doesn't count.

Isn't your pope the heretic George Bergoglio?